Theory of simple classical fluids: Universality in the short-range structure

Abstract

It is shown to within the accuracy of present-day computer-simulation studies that the bridge functions (i.e., the sum of elementary graphs, assumed zero in the hypernetted-chain approximation) constitute the same universal family of curves, irrespective of the assumed pair potential. In view of the known parametrized results for hard spheres, this observation introduces a new method in the theory of fluids, one that is applicable to any potential. The method requires the solution of a modified hypernetted-chain equation with inclusion of a one-parameter bridge-function family appropriate to hard spheres, and the single free parameter (the hard-sphere packing fraction) can be determined by appealing to the requirements of thermodynamic consistency. The assertion of universality is actually demonstrated via the application of this new method to a wide class of different potentials: e.g., hard spheres, Lennard-Jones, an inverse fifth power ($r^{-5\mathrm{}}$) applicable to the helium problem, the Coulomb potential (i.e., the one-component plasma), charged hard spheres, an oscillatory potential proposed for certain liquid metals, and the Yukawa potential.